Any suggestions from the group on how one could optically track a UAS using a powered telescope. The UAS transmits its coordinates and altitude to the base station how would one go about converting this to a x/y vector for the optical system? (this could also be used to keep a patch antenna aligned). What would be easiest approach to this?Any thoughts would be welcome.
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So based on what I wrote last night, I came up with a few formulas to calculate the vertical degree alignment and horizontal degree alignment. All you need to know is the latitude and longitude of your ground station, and the latitude, longitude, and altitude of your plane. I'm not very good at coding yet, so I'm not going to be able to tell you how to get any of this in a computer program/logic chip.
So here are the formulas:
First comes the horizontal alignment of your ground station, using the haversine formula... I can tell you where I looked up this formula, but I don't completely understand it, as I am not versed in spherical trigonometry.
finaldegrees is the final degrees you have to aim the ground station, so you can use this to control a servo, or you can *try* to eyeball it. 6373 is the radius of earth in km so if you want to experiment with your coding of it, keep that in mind.
and now for the vertical aim of the ground station...
dlat = lat2 - lat1
dlon = lon2 - lon1
a = (sin(dlat/2))^2+cos(lat1)*cos(lat2)*(sin(dlon/2))^2
b = 2*atan2(sqrt(a),sqrt(1-a))
c = 6373*b
d = altitude*0.0003048 NOTE: altitude is in feet and this converts it to km
e = tan(d/c)
f = (360*c)/40041.47
g = (180-f)/2
h = 90-g
finaldegrees = e-h
so its kind of long and has a few variables haha... it took me a while this morning to figure it out. These formulas account for the fact that the earth is not flat, and it takes that into account determining the horizontal degrees, and it even accounts the curvature of the earth for the vertical degrees.
If I made any mistakes (I don't think I did, I've checked it a few times) I apologize... any comments? advice on the coding of it?
EDIT: and btw for the formula atan2(x,y) it doesn't mean multiply (x,y) times 2. It is a weird function that I think is related to arctan.
So the simplest way to align a patch antenna is probably just through a code that tests signal strength. However, there are two problems with that, it doesn't work well enough to align a telescope, and the group of people on this sight don't seem to be satisfied with the simplest way to do things (the best way is more like it).
The formula to calculate the tilt of the antenna or telescope isn't simple as solving the triangle with the difference in lat and lon on 2 sides and using that number to solve the triangle for distance and altitude. The earth is (unfortunately for this purpose) not flat, so we cannot treat it as a 2D object. You must use the haversine formula to calculate the distance. The haversine formula allows you to calculate the distance between two points on a curved surface if you can draw a (slightly curvy :P ) triangle on it and you know a few of the angles and sides. Using the haversine formula for the ground distance makes the rest seem easy. All you do is solve the triangle with the sides of the altitude and ground distance. Unfortunately you still aren't there yet, depending on whether or not you have flown far away. If you are far away enough, you need to account for the curvature for the earth (if you want i can look up more on that later but I'm wrapping up my wall of text post). If your plane is close this doesn't matter, but if it is very far, it matters a great deal. For example, if you fly far away without accounting for earth curvature, your antenna or telescope may be pointed at say 10 deg, but when accounting for curvature, you may have your telescope or antenna pointed towards the ground. (note that you never want the antenna or telescope to be pointing close to ground level, as this means you are flying too and the plane will no longer be above the horizon.
All of the information above assumes you know the gps coordinates of the plane, and the gps coordinates of the ground station, along with the altitude of the plane, and height of the antenna or telescope.
I will gladly accept any questions, comments, and corrections.
Once made an optical tracker that used a pan/tilt mounted laser. The laser zigzag scanned a small area where the rover was & the rover sent back a signal when it received the laser. It could follow motion as long as the the scan pattern was faster than the rover & was cheap.
I've been thinking the same thing - Use my GPS downlink (via APRS) to point my tracking devices. While this is a secondary (terriary? quadrupinary??) projects idea for me I see the following components involved:
- GPS from the UAV
- The tracking stations' GPS location - Could be a value sent from the UAV while a button is pressed on the tracking station and the UAV is held above it.
- Orientation of the tracking array. This might mean placing it manually, or adding an electronic compass. I've been considering giving it its own GPS and compass so it can be placed in the back of a pickup truck while chasing high altitude balloon launches (www.hapb.net).
- Stepper motors which can give feedback on their orientation.
- A controller (al a the Propeller, Arduino or PIC, etc) to read the inputs and do the math, control the motors, fire the lasers, uhh I mean aim the antennas, etc. I saw a finished stepper motor+camera projects yesterday on the parallax forums so am posting it here: http://forums.parallax.com/forums/default.aspx?f=25&m=280948
I'd love to trivialize and say put them together and your off, but there's a bit more to the secret sauce!
The devil's in the details...
Paul
I'm actually doing just that for my patch antenna. Thus far i only have the materials list, as i haven't gone through the long/lat to 360* conversion equations yet. What you need is a compass for your telescope/patch antenna, aka "object", and some servo motors. You can "align" the object to north at the start of your pogram so that you have a point to start your calculations if you don't want to pay for an electronic compass. You need to know how many steps per degree or degree per steps, which you can find by using, or altering, this equations: (gear ratio*steps per revolution/360).
When i get that conversion stuff done, i'll let you know. its probably a simple equation, but right now, i'm about to go out.
Replies
Hi there!
I know this is an old tread but I read it and stumbled over this (link below) just a short while after...
http://mongrelgear.com.au/the-mongrels-shop.html?page=shop.product_...
(in case the link dosent work)
http://mongrelgear.com.au/the-mongrels-shop.html?page=shop.browse&a...
The principal is there...only modify it to fit you´re telescope!
Cheers /Brink, Sweden
So here are the formulas:
First comes the horizontal alignment of your ground station, using the haversine formula... I can tell you where I looked up this formula, but I don't completely understand it, as I am not versed in spherical trigonometry.
dlat = lat2 - lat1
latA = (sin(dlat/2))^2 + cos(lat1)*cos(lat2)*(sin(0))^2
latB = 2*atan2(sqrt(latA),sqrt(latA-1))
latC = 6373*latB
dlon = lon2 - lon1
lonA = (sin(0)^2 + cos(lat1)*cos(lat1)*sin(dlon/2)^2
lonB = 2*atan2(sqrt(lonA),sqrt(1-lonA))
lonC = 6373*lonB
finaldegrees = tan(latC/lonC)
finaldegrees is the final degrees you have to aim the ground station, so you can use this to control a servo, or you can *try* to eyeball it. 6373 is the radius of earth in km so if you want to experiment with your coding of it, keep that in mind.
and now for the vertical aim of the ground station...
dlat = lat2 - lat1
dlon = lon2 - lon1
a = (sin(dlat/2))^2+cos(lat1)*cos(lat2)*(sin(dlon/2))^2
b = 2*atan2(sqrt(a),sqrt(1-a))
c = 6373*b
d = altitude*0.0003048 NOTE: altitude is in feet and this converts it to km
e = tan(d/c)
f = (360*c)/40041.47
g = (180-f)/2
h = 90-g
finaldegrees = e-h
so its kind of long and has a few variables haha... it took me a while this morning to figure it out. These formulas account for the fact that the earth is not flat, and it takes that into account determining the horizontal degrees, and it even accounts the curvature of the earth for the vertical degrees.
If I made any mistakes (I don't think I did, I've checked it a few times) I apologize... any comments? advice on the coding of it?
EDIT: and btw for the formula atan2(x,y) it doesn't mean multiply (x,y) times 2. It is a weird function that I think is related to arctan.
The formula to calculate the tilt of the antenna or telescope isn't simple as solving the triangle with the difference in lat and lon on 2 sides and using that number to solve the triangle for distance and altitude. The earth is (unfortunately for this purpose) not flat, so we cannot treat it as a 2D object. You must use the haversine formula to calculate the distance. The haversine formula allows you to calculate the distance between two points on a curved surface if you can draw a (slightly curvy :P ) triangle on it and you know a few of the angles and sides. Using the haversine formula for the ground distance makes the rest seem easy. All you do is solve the triangle with the sides of the altitude and ground distance. Unfortunately you still aren't there yet, depending on whether or not you have flown far away. If you are far away enough, you need to account for the curvature for the earth (if you want i can look up more on that later but I'm wrapping up my wall of text post). If your plane is close this doesn't matter, but if it is very far, it matters a great deal. For example, if you fly far away without accounting for earth curvature, your antenna or telescope may be pointed at say 10 deg, but when accounting for curvature, you may have your telescope or antenna pointed towards the ground. (note that you never want the antenna or telescope to be pointing close to ground level, as this means you are flying too and the plane will no longer be above the horizon.
All of the information above assumes you know the gps coordinates of the plane, and the gps coordinates of the ground station, along with the altitude of the plane, and height of the antenna or telescope.
I will gladly accept any questions, comments, and corrections.
I've been thinking the same thing - Use my GPS downlink (via APRS) to point my tracking devices. While this is a secondary (terriary? quadrupinary??) projects idea for me I see the following components involved:
- GPS from the UAV
- The tracking stations' GPS location - Could be a value sent from the UAV while a button is pressed on the tracking station and the UAV is held above it.
- Orientation of the tracking array. This might mean placing it manually, or adding an electronic compass. I've been considering giving it its own GPS and compass so it can be placed in the back of a pickup truck while chasing high altitude balloon launches (www.hapb.net).
- Stepper motors which can give feedback on their orientation.
- A controller (al a the Propeller, Arduino or PIC, etc) to read the inputs and do the math, control the motors, fire the lasers, uhh I mean aim the antennas, etc. I saw a finished stepper motor+camera projects yesterday on the parallax forums so am posting it here:
http://forums.parallax.com/forums/default.aspx?f=25&m=280948
I'd love to trivialize and say put them together and your off, but there's a bit more to the secret sauce!
The devil's in the details...
Paul
When i get that conversion stuff done, i'll let you know. its probably a simple equation, but right now, i'm about to go out.